What is the Greatest Common Factor of 65997 and 66003?

Greatest common factor (GCF) of 65997 and 66003 is 3.

GCF(65997,66003) = 3

We will now calculate the prime factors of 65997 and 66003, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65997 and 66003.

How to find the GCF of 65997 and 66003?

We will first find the prime factorization of 65997 and 66003. After we will calculate the factors of 65997 and 66003 and find the biggest common factor number .

Step-1: Prime Factorization of 65997

Prime factors of 65997 are 3, 7333. Prime factorization of 65997 in exponential form is:

65997 = 3² × 7333¹

Step-2: Prime Factorization of 66003

Prime factors of 66003 are 3, 7, 449. Prime factorization of 66003 in exponential form is:

66003 = 3¹ × 7² × 449¹

Step-3: Factors of 65997

List of positive integer factors of 65997 that divides 65997 without a remainder.

1, 3, 9, 7333, 21999

Step-4: Factors of 66003

List of positive integer factors of 66003 that divides 65997 without a remainder.

1, 3, 7, 21, 49, 147, 449, 1347, 3143, 9429, 22001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65997 and 66003. The biggest common factor number is the GCF number.
So the greatest common factor 65997 and 66003 is 3.

Also check out the Least Common Multiple of 65997 and 66003